Question 778053
value of sin(a/2) if cos a=2/3 and 0 < a < 90º
use half-angle formula for sin:
{{{sin(a/2)=sqrt((1-cos(a))/2)=sqrt((1-(2/3))/2)=sqrt((1/3)/2)=1/sqrt(6)=sqrt(6)/6}}}
..
check:
cos(a)=2/3
a&#8776;48.19º
a/2&#8776;24.09º
sin(a/2)&#8776;sin(24.09º)&#8776;0.4082
exact value=&#8730;6/6&#8776;0.4082